Products to Sum

[rich lava]

A little stuck on how to even approach this question. Help would be greatly appreciated

[random hemlock]

maybe try to use the formula:
sin(a)+sin(b) = 2sin((a+b)/2)cos((a-b)/2)

[chilly cedar]

Start with :
$$S_n = \frac{1}{\sin(x)}\sum_{k=0}^{n-1}\sin(x)\sin((2k+1)x)$$

[twin palm]

Ævan

[rich lava]

oi w swindle helping me out again

[rich lava]

bro what

[rich lava]

yea tried that but got a second sequence

[chilly cedar]

I just multiplied by sin(x)/sin(x)=1

So you can apply the product to sum formula

[random hemlock]

@rich lava you can use this

2sin(a)sin(b) = cos(a-b)-cos(a+b)

compute the sum

then (1/2)(1-cos(2a)) = sin²(a)